Speed control works on small video, not on large
For whatever reason, the preview and the rendered short clips were played in realtime (1x), but when I ran the whole rendering, the result was sped up (10x) as I wanted -- so effectively, my problem was that I simply didn't commit to the full rendering job. I had hoped that a short render would confirm in minutes what the full, lengthy job would produce.

During my playing around with it, I tried @3pointedit's suggestion to break the clip into frames, which also worked. For other users new to Blender, what I did was first open the Properties window, ensure PNG was selected (at the bottom of this image), set my output path (I left it at the default of /tmp\), then clicked Render (top of the image):



Then from a new project, in the Video Sequence Editor, I clicked Add -> Image, browsed to my temp directory, and selected all images. As a new user, the Blender UI is very unintuitive, and with tens of thousands of frames, I can't drag to select them all -- you have to hit a (NOT CTRL+ a) to select all of them. Then they're loaded together as a single strip which can be manipulated like a video.